Multiobjective optimization of an industrial grinding operation under uncertainty

Multiobjective optimization of an industrial grinding operation under various parameter uncertainties is carried out in this work. Two sources of uncertainties considered here are related to the (i) parameters that are used inside a model representing the process under consideration and subjected to experimental and regression errors and (ii) parameters that express operators’ choice for assigning bounds in the constraints and operators prefer them to be expressed around some value rather than certain crisp value. Uncertainty propagation of these parameters through nonlinear model equations is reflected in terms of system constraints and objectives that are treated here using chance constrained fuzzy simulation based approach. Such problems are treated in literature using the standard two stage stochastic programming methodology that has a drawback of leading to combinatorial explosion with an increase in the number of uncertain parameters. This problem is overcome here using a combination of fuzzy and chance constrained programming approach that tackles the problem by representing and treating the uncertain parameters in a different manner. Simultaneous maximization of grinding circuit throughput and percent passing mid size fraction are studied here with upper bound constraints for various performance metrics for the grinding circuit, e.g. percent passing of fine and coarse size classes, percent solids in the grinding circuit final outlet stream and circulation load of the grinding circuit. Uncertain parameters considered are grindability indices of rod mill and ball mill, sharpness indices of primary and secondary cyclones and the respective upper bounds for the constraints mentioned above. The deterministic multiobjective grinding optimization model of Mitra and Gopinath [2004. Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm. Chem. Eng. Sci. 59, 385–396.] forms the basis of this work on which various effects of uncertain parameters are shown and analyzed in a Pareto fashion. Nondominated sorting genetic algorithm, NSGA II, a popular elitist evolutionary multiobjective optimization approach, is used for this purpose.